Why does life hate me? Question:
Directions: A large pizza at Tony's Pizzeria is a circle with a 14-inch diameter. Its
box is a rectangular prism that is 1 14
8 inches long, 1 14
8 inches wide, and 3
1
4
inches
tall. Your job is to design a crazy new shape for a large pizza. It can be any
irregular polygon shape, but it must have at least five sides.
Tony says he will make and sell your crazy pizza if you can prove the following:
• It is approximately the same area as the large pizza he sells now.
• It fits inside the large box listed above.
• It can be cut into 8‒12 equal-sized pieces.
Create one design for a crazy pizza that will meet all of Tony's requirements.
1. Create a representation of your design that includes measurements.
2. Prove mathematically, using appropriate formulas, that your design is
approximately the same surface area as Tony’s large pizza.
3. Prove mathematically, using appropriate formulas, that your pizza will fit in
the box.
4. Use diagrams or other models to prove that your design can be divided into
8‒12 equal-sized pieces. (Tip: You may use graph paper or the Virtual
Geoboard to show how your pizza can be divided into equal-sized pieces.)
Your design and proofs (model and mathematical) will be submitted as your
portfolio assessment.
Thanks to all the people who might answer me!
well, the area of a regular n-gon of diameter d is
n/2 r^2 sin(360°/n)
so see what you can do with that.
i'm still confused
I understand that you are looking for help in designing a crazy new shape for a large pizza that meets certain requirements. Here's a step-by-step guide to help you with each requirement:
1. Designing a crazy pizza shape:
To create a design for a crazy pizza shape, you need to come up with an irregular polygon shape with at least five sides. You can experiment with various shapes like pentagons, hexagons, or any other irregular shape that you find interesting. Make sure to sketch your design on paper or use a graphic design software to visualize it accurately.
2. Proving the surface area is approximately the same as Tony's pizza:
To prove mathematically that your pizza design has approximately the same surface area as Tony's large pizza, you can use the formula for the area of a circle. Since Tony's pizza has a 14-inch diameter, the radius would be half of that, which is 7 inches. Calculate the area of Tony's pizza using the formula A = πr² and record the value.
Once you have your design, calculate the area using the appropriate formulas for the shape you have chosen. Compare the area of your design with the area of Tony's pizza. If they are close or approximately the same, you can consider this requirement fulfilled.
3. Proving your pizza will fit in the box:
To prove mathematically that your pizza will fit inside the box, you need to compare the dimensions of your pizza with the dimensions of the box. The box is a rectangular prism with dimensions 1 1/8 inches long, 1 1/8 inches wide, and 3 1/4 inches tall. Ensure that your pizza's longest side is smaller than or equal to the length of the box, and that the other dimensions also fit within the given width and height. If your pizza fits within the box, you have met this requirement.
4. Proving your design can be divided into 8-12 equal-sized pieces:
To demonstrate that your design can be divided into 8-12 equal-sized pieces, you can use diagrams or models. A useful tool for this would be graph paper or a virtual geoboard, where you can show how your pizza can be divided into equal-sized pieces. Experiment with different shapes and cutting patterns to find a configuration that results in 8-12 equal-sized pieces.
Ensure that the shapes are not too complex and can be practically cut in real life. Use your chosen tool to create diagrams or models that clearly illustrate how the cutting can be done.
Once you have completed all the steps and met all the requirements, document your design and the mathematical proofs in your portfolio assessment. This will serve as evidence of your work and will allow you to present your crazy pizza design to Tony for consideration.
Good luck with your design and assessment!